Suppose we have the improper prior π(λ)∝e−aλ, λ∈R (and a≥0). Conditional on λ, we have observations X1, X2, ⋯, Xn ∼i.i.d N(λ,1). Compute the posterior distribution π(λ|X1,X2,…,Xn), then provide the following statistics on the posterior distribution.
Use SumXi for ∑nᵢ=1Xᵢ.